Question

in the figure shown below, for what value of (h) will (xy = xz)? four students attempted to solve the problem. select the student who found the correct value of (h).

student a:
(7h - 5 + 3h + 5 = 90)
(10h + 10 = 90)
(10h = 80)
(h = 8)

student b:
(7h - 5 + 3h + 5 = 90)
(10h = 90)
(h = 9)

student c:
(7h - 5 = 3h + 5)
(4h - 5 = +5)
(4h = 10)
(h = \frac{10}{4})
(h = \frac{5}{2}) or (2.5)

student d:
(7h - 5 = 3h + 5)
(10h - 5 = 5)
(10h = 10)
(h = 1)

Explanation:

Equate the segment lengths using the Angle Bisector Theorem

$$
LATEXBLOCK0
$$

Solve the linear equation for h

$$
LATEXBLOCK1
$$

Identify the student with the correct solution

$$ \text{Student C found } h = 2.5 \text{ using the correct equation } 7h - 5 = 3h + 5. $$

Answer:

• Student A
• Student B
• Student C (Correct answer)
• Student D